A plastic ocean kayak has a sealed interior filled with air (like a big hard-pla

Question

A plastic ocean kayak has a sealed interior filled with air (like a big hard-plastic balloon), so that the rider basically sits on top of the floating sealed object. The kayak encloses a total volume of 0.750 m^3 and has a mass of 50.0 kg when empty. Use 1030 kg/m^3 for the density of seawater. a. While the empty kayak floats in equilibrium on the surface of the ocean, what fraction of its volume is below the surface? Show your work and/or explain your reasoning. b. What is the maximum mass of passengers this particular kayak can support while still being able to float at the surface? Show your work and/or explain your reasoning. Check your answer for reasonableness: roughly how many adults does this correspond to?

Explanation / Answer

Here ,

V = 0.750 m^3

a) let the fraction of kayak inside the water surface is x

Now , Using Archimedes principle

weight of water displaced = weight of kayak

x * V * g * density of water = m * g

x * 0.750 * 1030 = 50

solving for x

x = 0.0647

the fraction is 0.0647

b)

let the maximum mass is m

m = (1 - 0.0647) * 1030

m = 963.3 Kg

the maximum mass of passenger can be 963.3 Kg

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